Recent advances on the interval distance geometry problem

Abstract

We discuss a discretization-based solution approach for a classic problem in global optimization, namely the distance geometry problem (DGP). We focus our attention on a particular class of the DGP which is concerned with the identification of the conformation of biological molecules. Among the many relevant ideas for the discretization of the DGP in the literature, we identify the most promising ones and address their inherent limitations to application to this class of problems. The result is an improved method for estimating 3D structures of small proteins based only on the knowledge of some distance restraints between pairs of atoms. We present computational results showcasing the usefulness of the new proposed approach. Proteins act on living cells according to their geometric and chemical properties: finding protein conformations can be very useful within the pharmaceutical industry in order to synthesize new drugs.

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    Continuous motions of part of the structure preserving all distance restraints.

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Acknowledgements

DG and CL are thankful to the Brazilian research agencies FAPESP and CNPq for partial financial support. LL was partially supported by the “Bip:Bip” project within the ANR “Investissement d’Avenir” program. AM thanks University of Rennes 1 for financial support. AM and DG also acknowledge Brittany Region (France) for partial financial support.

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Correspondence to Leo Liberti.

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Gonçalves, D.S., Mucherino, A., Lavor, C. et al. Recent advances on the interval distance geometry problem. J Glob Optim 69, 525–545 (2017). https://doi.org/10.1007/s10898-016-0493-6

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Keywords

  • Distance geometry
  • Discretization
  • Molecular conformation